Class 10 Exam > Class 10 Questions > A stone is falling freely from rest and the t...
Start Learning for Free
A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?
Verified Answer
A stone is falling freely from rest and the total distance covered by ...
The distance travelled by the stone in the nth second is given by,
.png)
5th second is the last second. So, the stone will remain in air for 5 seconds.
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
A stone is falling freely from rest and the total distance covered by ...
The Problem
A stone is falling freely from rest, and we need to determine how long it remains in the air. We are given that the distance covered by the stone in the last second of its motion is equal to the distance covered in the first 3 seconds.
Analysis
Let's break down the problem and analyze it step by step.
1. Initial Motion
- The stone is falling freely from rest, which means it starts from rest and falls under the influence of gravity.
- We can apply the equation of motion:
- Distance covered, s = ut + 0.5 * a * t^2, where u is initial velocity, a is acceleration, and t is time.
- Since the stone starts from rest, the initial velocity (u) is 0.
2. First 3 Seconds
- We are given that the distance covered in the first 3 seconds is equal to the distance covered in the last second.
- Let's represent the distance covered in the first 3 seconds as s1 and the distance covered in the last second as s2.
- According to the given condition, s1 = s2.
3. Last Second of Motion
- Let's consider the last second of motion, from t = 2s to t = 3s.
- As per the given condition, the distance covered in this one-second interval is equal to the distance covered in the first 3 seconds.
- We can represent this distance as s2 = s1.
4. Calculating Distance Covered
- To calculate the distance covered in the first 3 seconds, we substitute t = 3s in the equation of motion.
- s1 = 0 + 0.5 * a * (3^2) = 4.5a.
- Similarly, for the last second, s2 = 0 + 0.5 * a * (1^2) = 0.5a.
5. Equating Distances
- As per the given condition, s1 = s2.
- 4.5a = 0.5a.
- Dividing both sides by a gives us 4.5 = 0.5.
- This is not possible unless a = 0.
- Therefore, the acceleration (a) must be zero.
6. Duration of Motion
- If the acceleration is zero, it means the stone is not experiencing any external force and is moving with a constant velocity.
- The stone will continue to move at this constant velocity until it hits the ground.
- Since there is no acceleration, the stone will remain in the air indefinitely.
Conclusion
In this problem, we found that the stone remains in the air indefinitely. This is because the distance covered in the first 3 seconds is equal to the distance covered in the last second, which is only possible when the acceleration is zero. Therefore, the stone continues to move with a constant velocity until it hits the ground.
A stone is falling freely from rest, and we need to determine how long it remains in the air. We are given that the distance covered by the stone in the last second of its motion is equal to the distance covered in the first 3 seconds.
Analysis
Let's break down the problem and analyze it step by step.
1. Initial Motion
- The stone is falling freely from rest, which means it starts from rest and falls under the influence of gravity.
- We can apply the equation of motion:
- Distance covered, s = ut + 0.5 * a * t^2, where u is initial velocity, a is acceleration, and t is time.
- Since the stone starts from rest, the initial velocity (u) is 0.
2. First 3 Seconds
- We are given that the distance covered in the first 3 seconds is equal to the distance covered in the last second.
- Let's represent the distance covered in the first 3 seconds as s1 and the distance covered in the last second as s2.
- According to the given condition, s1 = s2.
3. Last Second of Motion
- Let's consider the last second of motion, from t = 2s to t = 3s.
- As per the given condition, the distance covered in this one-second interval is equal to the distance covered in the first 3 seconds.
- We can represent this distance as s2 = s1.
4. Calculating Distance Covered
- To calculate the distance covered in the first 3 seconds, we substitute t = 3s in the equation of motion.
- s1 = 0 + 0.5 * a * (3^2) = 4.5a.
- Similarly, for the last second, s2 = 0 + 0.5 * a * (1^2) = 0.5a.
5. Equating Distances
- As per the given condition, s1 = s2.
- 4.5a = 0.5a.
- Dividing both sides by a gives us 4.5 = 0.5.
- This is not possible unless a = 0.
- Therefore, the acceleration (a) must be zero.
6. Duration of Motion
- If the acceleration is zero, it means the stone is not experiencing any external force and is moving with a constant velocity.
- The stone will continue to move at this constant velocity until it hits the ground.
- Since there is no acceleration, the stone will remain in the air indefinitely.
Conclusion
In this problem, we found that the stone remains in the air indefinitely. This is because the distance covered in the first 3 seconds is equal to the distance covered in the last second, which is only possible when the acceleration is zero. Therefore, the stone continues to move with a constant velocity until it hits the ground.
Community Answer
A stone is falling freely from rest and the total distance covered by ...
6 seconds
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?
Question Description
A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?.
A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?.
Solutions for A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? defined & explained in the simplest way possible. Besides giving the explanation of
A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air?, a detailed solution for A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? has been provided alongside types of A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? theory, EduRev gives you an
ample number of questions to practice A stone is falling freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first 3 seconds of its motion. How long does the stone remain in air? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup